PIM and DM discrepancies

[simone77]

To me this is a recurrent situation when passing from PIM structure to DM (for example to model additive effects).
According to my personal experience, to other analogous topics in this Forum (see this for a very similar thread) and to GM, I know that often discrepancies arise from the kind of link function used, to reference code used in DM (PIM uses first interval as reference code) and to the wrong structure of the DM.

In this case I really don't understand what is going on.
I am working in a CJS context and have an age model both for phi and p (this is an age model given individuals are marked only by chicks). There are 11 occasions and, in this case, just one group.
So this is how my DM looks like (the part for p is identical):


Initially I used the Logit link for both the PIM and the DM (starting from the identity DM with respect to the model run in PIM) and found very different values of deviances. So I tried to modify the DM with several other structures that I thought to be equivalent (mainly by using different reference codes) and found always the same identical value for deviance that, as said, was very different from that of PIM model.
After lot of trials I tried to use the Sin link for the PIM and, surprise to me, I got the same identical deviance obtained with the Logit link in DM. Here below there is the result browser, the number of parameters have been corrected according to what I think that should be the number of estimable parameters.


I'm convinced there is something more to learn and that it has a logical explication.

After this, question inside the question: in this analyses the number of estimable parameters in MARK tended to be always more than I thought, for instance the model 3 had 36 estimable parameters, 8 more than I think it would be correct. I thought that MARK may loose some parameters, i.e., say there are less estimable parameters than there are really, but this time it seems to be high-biased: is it "normal"?

Thanks in advance for any help,

Simone

[cooch]

To me this is a recurrent situation when passing from PIM structure to DM (for example to model additive effects).
According to my personal experience, to other analogous topics in this Forum (see this for a very similar thread) and to GM, I know that often discrepancies arise from the kind of link function used, to reference code used in DM (PIM uses first interval as reference code) and to the wrong structure of the DM.

In this case I really don't understand what is going on.

Problem is specific to your data. Structurally, the models are equivalent. If you get differences in deviance among the models you've tried, its because of issues with the data. This commonly occurs when you have one or more parameters that are poorly estimated. Nothing more.

After this, question inside the question: in this analyses the number of estimable parameters in MARK tended to be always more than I thought, for instance the model 3 had 36 estimable parameters, 8 more than I think it would be correct. I thought that MARK may loose some parameters, i.e., say there are less estimable parameters than there are really, but this time it seems to be high-biased: is it "normal"?

Thanks in advance for any help,

Simone

Your statement that parameter counts is 'biased high' reflects lack of understanding on your part. 11 occasions, 2 age classes, full time-dependence in each age class for both phi and p = 38 structural parameters. Terminal phi and p are confounded for both age classes, so, 38 - 2 = 36 parameters. MARK won't report more than this. If it does, something is wrong with how you've built the model. I it reports less, problems is likely your data.

[simone77]

Thank you for the reply.
I had no idea that discrepancies between DM and PIM might be due to issues with the data. Also, I guess it is not casual that DM with Logit gives identical deviances to PIM with Sin link, is there a simple to explain reason for that?
Anyway, good to know it!

Now I wonder in these cases how one should deal with this, I mean, if I am interested in running additive models perhaps I should work just with DM to make AIC ranking meaningful, do you agree with that?

Regarding my wrong parameter count, thanks to make me see that. Really it has not been a problem of lack of understanding, but a problem with arithmetic sums . In fact I would consider 9 phis for age class 1, 8 phis for age class 2, the same for ps and two betas (one for age class 1, another one for age class 2), so:
9+8+9+8+2=36